95   several external SAT solvers will be tried (assuming they are installed).   | 
    95   several external SAT solvers will be tried (assuming they are installed).   | 
    96   If no external SAT solver is installed, then the default is   | 
    96   If no external SAT solver is installed, then the default is   | 
    97   @{text [quotes] "dpll"}. | 
    97   @{text [quotes] "dpll"}. | 
    98   | 
    98   | 
    99   There are also two tactics that make use of SAT solvers. One   | 
    99   There are also two tactics that make use of SAT solvers. One   | 
   100   is the tactic @{ML sat_tac in sat}. For example  | 
   100   is the tactic @{ML sat_tac in SAT}. For example  | 
   101 *}  | 
   101 *}  | 
   102   | 
   102   | 
   103 lemma "True"  | 
   103 lemma "True"  | 
   104 apply(tactic {* sat.sat_tac @{context} 1 *}) | 
   104 apply(tactic {* SAT.sat_tac @{context} 1 *}) | 
   105 done  | 
   105 done  | 
   106   | 
   106   | 
   107 text {* | 
   107 text {* | 
   108   However, for proving anything more exciting using @{ML "sat_tac" in sat} you  | 
   108   However, for proving anything more exciting using @{ML "sat_tac" in SAT} you  | 
   109   have to use a SAT solver that can produce a proof. The internal   | 
   109   have to use a SAT solver that can produce a proof. The internal   | 
   110   one is not usuable for this.   | 
   110   one is not usuable for this.   | 
   111   | 
   111   | 
   112   \begin{readmore}  | 
   112   \begin{readmore}  | 
   113   The interface for the external SAT solvers is implemented  | 
   113   The interface for the external SAT solvers is implemented  | 
   114   in @{ML_file "HOL/Tools/sat_solver.ML"}. This file contains also a simple | 
   114   in @{ML_file "HOL/Tools/sat_solver.ML"}. This file contains also a simple | 
   115   SAT solver based on the DPLL algorithm. The tactics for SAT solvers are  | 
   115   SAT solver based on the DPLL algorithm. The tactics for SAT solvers are  | 
   116   implemented in @{ML_file "HOL/Tools/sat_funcs.ML"}. Functions concerning | 
   116   implemented in @{ML_file "HOL/Tools/sat.ML"}. Functions concerning | 
   117   propositional formulas are implemented in @{ML_file | 
   117   propositional formulas are implemented in @{ML_file | 
   118   "HOL/Tools/prop_logic.ML"}. The tables used in the translation function are  | 
   118   "HOL/Tools/prop_logic.ML"}. The tables used in the translation function are  | 
   119   implemented in @{ML_file "Pure/General/table.ML"}.   | 
   119   implemented in @{ML_file "Pure/General/table.ML"}.   | 
   120   \end{readmore} | 
   120   \end{readmore} | 
   121 *}  | 
   121 *}  |